Find the hypotenuse with the legs of a right triangle 6cm and 8cm.

First of all, you should remember how you can find the hypotenuse of a right triangle if the lengths of its two legs are known. The Pythagorean theorem will help us with this, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

c ^ 2 = a ^ 2 + b ^ 2.

Substitute here the values a = 6 cm and b = 8 cm and we get:

c ^ 2 = 6 ^ 2 + 8 ^ 2;

c ^ 2 = 6 * 6 + 8 * 8;

c ^ 2 = 36 + 64;

c ^ 2 = 100.

Therefore, the length of the hypotenuse is:

c = √100 = √ (10 ^ 2) = 10.

Answer: with legs 6 and 8 cm, the hypotenuse is 10 cm.